Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in
magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let X be a random variable that represents a magnetic
susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the
table below. Magnetic Susceptibility Readings,
centimeter- ram-second x 10'6 cm x 10" Magnetic Number of Estimated
Comment Susceptibility Readings Probability
"cool" 0 S X < 10 36 36/120 = 0.30
"neutral" 10 S X < 20 48 48/120 = 0.40
"warm" 20 S X < 30 12 12/120 = 0.10
"very interesting" 30 s x < 40 18 18/120 = 0.15
"hot spot" 40 s X 6 6/120 = 0.05 Suppose a reading between 30 and 40 is called "very interesting" from an archaeological point of view. Let us say you take readings at n = 12 sites
chosen at random. Let r be a binomial random variable that represents the number of "very interesting" readings from these 12 sites. (a) Let us call "very interesting" a binomial success. Use the table above to find p, the probability of success on a single trial, where
p = P(success) = P(30 s x < 40). (b) What is the expected value p and standard deviation 0 for the random variable r? (Round your standard deviation to three decimal places.)
,1 = a: (c) What is the probability that you will find at least one "very interesting" reading in the 12 sites? (Round your answer to three decimal places.) (d) What is the probability that you will find fewer than three "very interesting" readings in the 12 sites? (Round your answer to three decimal
places.)